The iOS 7 rush is causing lots of problems for a lot of people.
iOS 7 downloaded fine for me but then I received a “Software Update Failed” message.
Follow these steps and your problems will be solved:
1. Restart your device.
2. Disable your Wi-Fi.
3. Turn off your device and keep it off for 5 minutes.
4. Turn your device back on and enable Wi-Fi.
5. Try the download again.
It sounds simple but it has worked 100% of the time for the people I’ve told about it.
Feel free to share this fix on Facebook or tweet about it on Twitter to help others getting this error.